K Prototype of kaonic nuclei Kpp 1 Introduction

K-中間子原子核、最近の状況 Prototype of kaonic nuclei “K-pp” 1. Introduction • • KEK Theory center J-PARC branch /IPNS Akinobu Doté Expanding the nuclear world Exotic properties of kaonic nuclei with a phenomenological Kbar. N potential Y. Akaishi (Nihon/RIKEN), T. Yamazaki (RIKEN) 2. Variational calculation of K-pp with a chiral SU(3)-based Kbar. N potential T. Hyodo (TITech), W. Weise (TU Munich) 3. Current status of the K-pp study 4. Experiments related to Kbar nuclear physics 5. Summary and future plan 東大駒場セミナー 　’ 12. 05. 23 @ 東京大学駒場キャンパス

1. Introduction

Expanding the nuclear world 原子核 ＝ 陽子・中性子からなる有限量子多体系、　安定核　…　約３００種 Large isospin 　　　　不安定核…約3000種、RIBF＠理研で展開 http: //www. rarf. riken. go. jp/newcontents/facility/RIBF. html

Kaonic nuclei Another form of nuclear system with strangeness K- Nucleus containing K- meson

What is Kaonic nucleus? Hypernuclei… d u s Hyperon baryon = qqq Nucleus Strangeness is introduced through baryons.

What is Kaonic nucleus? Strangeness is introduced through mesons … ubar s K- meson = qqbar quark (q) and anti-quark (qbar) pair Nucleus Kaonic nuclei !

Actors in Kbar nuclei Energy [Me. V] Leading actors Key person 1435 1405 p + KΛ(1405) 1325 Σ+π 1250 Λ+π 1190 Σ 1115 Λ Excited state of Λ Supporting players 940 p, n

Mysterious state; Λ(1405) Quark model prediction … calculated as 3 -quark state Λ(1405) can’t be well reproduced as a 3 -quark state! calculated Λ(1405) observed Λ(1405) q qq N. Isgar and G. Karl, Phys. Rev. D 18, 4187 (1978)

Actors in Kbar nuclei Energy [Me. V] Leading actors Key person p + KΛ(1405) 1435 1405 1325 Σ + π- bound state I=0 Proton-K with 30 Me. V binding energy? 1250 　Not 3 quark Λ + πstate? 　　←　can’t be explained with 　　　　　a simple quark model… Σ 1190 Λ 1115 Excited state of Λ Supporting players 940 q qq p, n u ud ubar s

Actors in Kbar nuclei Energy [Me. V] Leading actors Key person 1435 1405 p + KΛ(1405) 1325 Σ+π 1250 1190 Λ+π Σπ channel is open at about 100 Me. V below Σ the Proton-K- threshold. Λ 1115 Excited state of Λ Supporting players 940 p, n

Interests of Kaonic nuclei Kaonic nucleus Proton K- = K- • Nuclear structure change. Highly dense state. if the interaction is so attractive… Λ(1405) ü Deeply • Self-bound Kbar-nuclear system bound below πΣ threshold (main decay channel) KNNN… Possible to exist as a quasi-bound state with narrow width ΣπNN… K nuclear state

Studies with a phenomenological Kbar. N potential • Y. Akaishi and T. Yamazaki, PRC 52, 044005 (2002) Phenomenological Kbar. N potential (AY Kbar. N potential) 1. Free Kbar. N scattering data 2. 1 s level shift of kaonic hydrogen atom 3. Binding energy and width of Λ(1405) Strongly attractive Λ(1405) = I=0 K- p quasi-bound state with 27 Me. V binding energy 3 He. K- … 100 Me. V binding with a narrow width of 20 Me. V. (a simple model calculation) Deeply bound kaonic nuclei ! • A. D. , H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590, 51 (2004); PRC 70, 044313 (2004) Systematic study of light kaonic nuclei (3 He. K- to 11 CK-) with AMD + G-matrix (effective NN potential ) + AY Kbar. N potential shows their interesting properties…

①　Deeply bound ②　Drastic change and Dense of structure 8 Be ③　Isovector deformation 8 Be. K- ④　Proton satellite ppp. K-

Theoretical studies of nuclear system with anti-kaons • Light nuclei with a single antikaon 3 He. K- ～ 11 CK- studied with AMD + G-matrix + AY potential E(K)≒ 100 Me. V • Light nuclei with double antikaons 3 He. K-K- etc studied with AMD + G-matrix + AY potential E(2 K)≒ 200 Me. V • Medium to heavy nuclei with multi-antikaons Studied with Relativistic Mean Field - D. Gazda, E. Friedman, A. Gal and J. Mares, PRC 76, 055204 (2007); PRC 77, 045206 (2008) - T. Muto, T. Maruyama and T. Tatsumi, PRC 79, 035207 (2009) … Antikaon part is based on non-linear chiral Lagrangian Strongly repulsive Kbar interaction Saturation for the number of antikaons In case of 15 O+x. K-, central nuclear density and –B/x are saturated for x>8. • Nuclear matter with antikoans Neutron star, kaon condensation…

2. Variational calculation of K pp with a chiral SU(3)-based bar K N potential

Are kaonic nuclei really exotic? • The phenomenological Kbar. N potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. AY potential Chiral SU(3) Kbar. N πΣ ηΛ KΞ

Are kaonic nuclei really exotic? • The phenomenological Kbar. N potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. • The G-matrix treatment is adequate? NN repulsive core is too smoothed out? As a result, such a dense state is formed? ?

More theoretical study of the most essential kaonic nucleus K-pp system “Prototype of kaonic nuclei” studied with a chiral SU(3)-based Kbar. N potential

K-pp Variational calculation of with a chiral SU(3)-based Kbar. N potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A 804, 197 (2008) Phys. Rev. C 79, 014003 (2009) ü Av 18 NN potential … a realistic NN potential with strong repulsive core (3 Ge. V). 1 E Strong repulsive core (3 Ge. V)

K-pp Variational calculation of with a chiral SU(3)-based Kbar. N potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A 804, 197 (2008) Phys. Rev. C 79, 014003 (2009) ü Av 18 NN potential … a realistic NN potential with strong repulsive core (3 Ge. V). ü Effective Kbar. N potential based on Chiral SU(3) theory … reproduce the original Kbar. N scattering amplitude obtained with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential

Local Kbar. N potential based on Chiral SU(3) I=0 Kbar. N scattering amplitude T. Hyodo and W. Weise, PRC 77, 035204(2008) Chiral Unitary Effective potential In Chiral unitary model, Resonance position in I=0 Kbar. N channel 1420 Me. V not 1405 Me. V ! 1420 Chiral unitary; T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C 68, 018201 (2003)

K-pp Variational calculation of with a chiral SU(3)-based Kbar. N potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A 804, 197 (2008) Phys. Rev. C 79, 014003 (2009) ü Av 18 NN potential … a realistic NN potential with strong repulsive core (3 Ge. V). ü Effective Kbar. N potential based on Chiral SU(3) theory … reproduce the original Kbar. N scattering amplitude I=0 Kbarobtained N resonance “Λ(1405)”appears with coupled channel chiral dynamics. at 1420 Me. V, not 1405 Me. V Single channel, Energy dependent, Complex, Gaussian-shape potential ü Variational method … Trial wave function contains NN/Kbar. N correlation functions. The NN repulsive core can directly be treated. Kbar N N

K-pp Variational calculation of with a chiral SU(3)-based Kbar. N potential A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A 804, 197 (2008) Phys. Rev. C 79, 014003 (2009) ü Av 18 NN potential … a realistic NN potential with strong repulsive core (3 Ge. V). ü Effective Kbar. N potential based on Chiral SU(3) theory … reproduce the original Kbar. N scattering amplitude I=0 Kbarobtained N resonance “Λ(1405)”appears with coupled channel chiral dynamics. at 1420 Me. V, not 1405 Me. V Single channel, Energy dependent, Complex, Gaussian-shape potential ü Variational method … Trial wave function contains NN/Kbar. N correlation functions. The NN repulsive core can directly be treated. Four variants of chiral unitary modes Total B. E. G（Kbar. N→p. Y） × : 20 ± 3 Me. V : 40 ～ 70 Me. V Shallow binding and large decay width

Kbar. N potential based on “HNJH” Structure of K-pp “Corrected”, Kbar N N

Kbar. N potential based on “HNJH” Structure of K-pp “Corrected”, Kbar K-pp中の二核子は普通の原子核の断片！ 1. 97 fm 通常核密度に対応していると思える。 N N 2. 21 fm NN distance in normal nuclei ～ 2 fm Size of deuteron ～ 4 fm

Kbar. N potential based on “HNJH” Structure of K-pp “Corrected”, Kbar 1. 97 fm N ü NN distance = 2. 21 fm Kbar. N distance = 1. 97 fm ü Mixture of TN=0 component = 3. 8 % N

Kbar. N potential based on “HNJH” Structure of K-pp “Corrected”, I=0 Kbar. N 1. 82 fm Kbar N ü NN distance = 2. 21 fm Kbar. N distance = 1. 97 fm ü Mixture of TN=0 component = 3. 8 % N

Kbar. N potential based on “HNJH” Structure of K-pp I=0 Kbar. N 1. 82 fm I=1 Kbar. N “Corrected”, Kbar 2. 33 fm N ü NN distance = 2. 21 fm Kbar. N distance = 1. 97 fm ü Mixture of TN=0 component = 3. 8 % N

Kbar. N potential based on “HNJH” Structure of K-pp I=0 Kbar. N 1. 82 fm “Corrected”, “Λ(1405)” as I=0 Kbar. N calculated with this potential I=1 Kbar. N 2. 33 fm 1. 86 fm Kbar Almost “Λ(1405)” N ü NN distance = 2. 21 fm Kbar. N distance = 1. 97 fm ü Mixture of TN=0 component = 3. 8 % N

Kbar. N potential based on “HNJH” “Corrected”, Structure of K-pp Density distribution: Kbar. N pair in K-pp vs “L(1405)” “Λ(1405)” Kbar Isospin 0 Kbar. N pair N Isospin 0 “K-pp ” N Isospin 1 Kbar. N pair Kbar N Isospin 0 and 1 mixed “L(1405)” almost survives in K-pp!

K-pp Variational calculation of with a chiral SU(3)-based Kbar. N potential ü s-wave Kbar. N potential (Variational calculation) B. E. 20 ± 3 Me. V • Dispersive correction (Effect of imaginary part) +6～ +18 Me. V • p-wave Kbar. N potential ～ -3 Me. V • Two nucleon absorption A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A 804, 197 (2008) Phys. Rev. C 79, 014003 (2009) Width 40 ～ 70 Me. V 10 ～ 35 Me. V 4～ 12 Me. V K-pp … Rough estimation Total B. E. 20 ～ 40 Me. V Total Width 55 ～ 120 Me. V Very large…

3. Current status of the K pp study

Kbar nuclei = Exotic system !? To make the situation more clear … K-pp= Prototye of Kbar nuclei Studied with various methods, because it is a three-body system: • Doté, Hyodo, Weise • Akaishi, Yamazaki • Ikeda, Sato • Shevchenko, Gal , Mares • Wycech, Green Variational with a chiral SU(3)-based ATMS with a phenomenological Faddeev with a chiral SU(3)-derived Faddeev with a phenomenological All calculations predict that Variational with a phenomenological K • Arai, Yasui, Oka Λ* nuclei model continued by Uchino, Hyodo, Oka • Nishikawa, Kondo Skyrme model Kbar. N potential K-pp bar. N PRC 79, 014003(2009) PRC 76, 045201(2007) PRC 76, 035203(2007) PRC 76, 044004(2007) can be bound. potential (with p-wave) PRC 79, 014001(2009) PTP 119, 103(2008) PRC 77, 055202(2008) There are several experiments: Experiments concerned to this topics: FINUDA (Frascatti), KEK, DISTO (Sacley), OBELIX (CERN) Planned or undergoing experiments: FOPI (GSI), J-PARC, AMADEUS (Frascatti)

Recent results of calculation of K-pp and related experiments Width (Kbar. NN→πYN) [Me. V] 0 20 40 60 80 100 120 140 0 Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) -20 -40 -60 Akaishi, Yamazaki [2] (Variational, Phenomenological) - B. E. [Me. V] -80 Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) Ikeda, Sato [4] (Faddeev, Chiral SU(3)) -100 -120 -140 [1] PRC 79, 014003 (2009) [2] PRC 76, 045201 (2007) [3] PRC 76, 044004 (2007) [4] PRC 76, 035203 (2007) Exp. : FNUDA [5] if it is a K-pp bound state. [5] PRL 94, 212303 (2005) [6] PRL 104, 132502 (2010) Exp. : DISTO [6] if it is a K-pp bound state. Using S-wave Kbar. N potential constrained by experimental data. … Kbar. N scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc.

Recent results of calculation of K-pp and related experiments Width (Kbar. NN→πYN) [Me. V] 0 20 40 60 80 100 120 140 0 Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) -20 -40 - B. E. Akaishi, Yamazaki [2] (Variational, Phenomenological) Wycech, Green [7] -60 (Variational, phenomenological, [Me. V] P-wave) Ikeda, Sato [4] -80 (Faddeev, Chiral SU(3)) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) -100 -120 -140 [1] PRC 79, 014003 (2009) [2] PRC 76, 045201 (2007) [3] PRC 76, 044004 (2007) [4] PRC 76, 035203 (2007) Exp. : FNUDA [5] if it is a K-pp bound state. [5] PRL 94, 212303 (2005) [6] PRL 104, 132502 (2010) Exp. : DISTO [6] if it is a K-pp bound state. Using S-wave Kbar. N potential constrained by experimental data. [7] PRC 79, 014001 (2009) … Kbar. N scattering data, Including P-wave Kbar. N potential, Kaonic hydrogen atom data, and other effects. “Λ(1405)” etc.

Recent results with various calculations of K-pp B. E. DHW 20 ± 3 Γ (mesonic) 40 ～ 70 Method Variational Kbar. N Int. Chiral SU(3) AY 47 61 Variational Phenom. IS 60 ～ 95 45 ～ 80 Faddeev (AGS) Chiral SU(3) (Separable) SGM Exp. FINUDA DISTO 50～ 70 90 ～ 110 Faddeev (AGS) Phenom. (Separable) Channels at final step Kbar. N, πY 115± 7 67± 14 K- absorption, Λp inv. mass 103± 3± 5 118± 8± 10 p+p→K++Λ+p, Λp inv. mass (Finalized) All four calculations shown above are constrained by experimental data. … Kbar. N scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Only s-wave Kbar. N potential is used.

Recent results with various calculations of K-pp B. E. DHW 20 ± 3 Γ (mesonic) 40 ～ 70 Method Variational Kbar. N Int. Chiral SU(3) AY 47 61 Variational Phenom. IS 60 ～ 95 45 ～ 80 Faddeev (AGS) Chiral SU(3) (Separable) SGM 50～ 70 90 ～ 110 Faddeev (AGS) Channels at final step Kbar. N, πY Phenom. (Separable) DHW vs AY Difference of the used Kbar. N interactions. Kbar. N, πY

Comparison of AY potential and Chiral-based potential Coupled channel Chiral dynamics AY potential Weinberg-Tomozawa term derived from Chiral SU(3) effective Lagrangian Two poles (double pole); one couples strongly to Kbar. N, Kbar. N strongly πΣ ηΛto πΣ. KΞ the other couples Λ(1405) = a quasi-bound state of I=0 Kbar. N at 1405 Me. V. Appears in I=0 Kbar. N channel. Λ(1405) (experimentally observed) appears in I=0 πΣ-πΣ channel. I=0 Kbar. N resonance @ 1420 Me. V. I=0 Kbar. N resonance @ 1405 Me. V. • Energy independent potential • No πΣ-πΣ interaction • Energy dependent potential • Somewhat strongly attractive πΣ-πΣ interaction

Comparison of AY potential and Chiral-based potential I=0 Kbar. N full scattering amplitude Quite different in the sub-threhold region Almost same in the on-shell region

Recent results with various calculations of K-pp B. E. DHW 20 ± 3 Γ (mesonic) 40 ～ 70 Method Variational Kbar. N Int. Chiral SU(3) AY 47 61 Variational Phenom. IS 60 ～ 95 45 ～ 80 Faddeev (AGS) Chiral SU(3) (Separable) SGM 50～ 70 90 ～ 110 Faddeev (AGS) Phenom. (Separable) Channels at final step Kbar. N, πY DHW vs AY In Chiral SU(3) theory, the πΣ-πΣ interaction is so attractive to make a resonance, while AY potential doesn’t have it. “Λ(1405)” is I=0 Kbar. N bound state at 1420 Me. V or 1405 Me. V? AY potential is twice more attractive than Chiral-based one.

Recent results with various calculations of K-pp B. E. DHW 20 ± 3 Γ (mesonic) 40 ～ 70 Method Variational Kbar. N Int. Chiral SU(3) AY 47 61 Variational Phenom. IS 60 ～ 95 45 ～ 80 Faddeev (AGS) Chiral SU(3) (Separable) SGM 50～ 70 90 ～ 110 Faddeev (AGS) Phenom. (Separable) Channels at final step Kbar. N, πY DHW vs IS Although both are based on Chiral SU(3) theory, results are very different from each other. • Separable approximation? • Different energy dependence of interaction kernel Vij? • πΣN three-body dynamics … may not be included in DHW. (Y. Ikeda and T. Sato, PRC 79, 035201(2009))

Variational cal. vs Faddeev A possible reason is Y. Ikeda and T. Sato, PRC 79, 035201(2009) πΣN thee-body dynamics Three-body system calculated with the effective Kbar. N potential K K N N K = N conserved N N π Σ … π Σ N In the variational calculation (DHW), πΣ channel is eliminated and incorporated into the effective Kbar. N potential. K N N +…

4. Experiments related to bar K nuclear physics

Ｋ原子核に関係する実験 u Ｋ原子 (Kaonic atom) • Kaonic 4 He atom, 2 pレベルシフト (3 d→ 2 p X線測定) @ KEK (E 570) S. Okada et. al. , Phys. Lett. B 653, 387 (2007) • Kaonic 3 He atom, 2 pレベルシフト (3 d→ 2 p X線測定) @ J-PARC (E 17, DAY-1) • Kaonic hydrogen atom, 1 sレベルシフト @ DEAR group, DAΦNE, G. Beer et al. , Phys. Rev. Lett. 94, 212302 (2005) Frascati National Laboratories • Kaonic hydrogen, deuterium @ SIDDHARTA group M. Bazzi et al. , Phys. Lett. B 704, 113 (2011) u Λ(1405) πΣ invariant mass測定 γ + p → K+ + Λ(1405), Λ(1405) → π Σ • LEPS / SPring-8 J. K. Ahn, Nucl. Phys. A 835, 329 (2010) K. Moriya and R. Schumacher, Nucl. Phys. A 835, 325 (2010) • CLAS / JLab π-Σ+, π0Σ 0, π+Σ- が全て押さえられた

Ｋ原子核に関係する実験 u Ｋ原子 (Kaonic atom) • Kaonic 4 He atom, 2 pレベルシフト (3 d→ 2 p X線測定) @ KEK (E 570) S. Okada et. al. , Phys. Lett. B 653, 387 (2007) • Kaonic 3 He atom, 2 pレベルシフト (3 d→ 2 p X線測定) @ J-PARC (E 17, DAY-1) • Kaonic hydrogen atom, 1 sレベルシフト @ DEAR group, DAΦNE, G. Beer et al. , Phys. Rev. Lett. 94, 212302 (2005) Frascati National Laboratories • Kaonic hydrogen, deuterium @ SIDDHARTA group M. Bazzi et al. , Phys. Lett. B 704, 113 (2011) u Λ(1405) πΣ invariant mass測定 γ + p → K+ + Λ(1405), Λ(1405) → π Σ • LEPS / SPring-8 J. K. Ahn, Nucl. Phys. A 835, 329 (2010) K. Moriya and R. Schumacher, Nucl. Phys. A 835, 325 (2010) • CLAS / JLab π-Σ+, π0Σ 0, π+Σ- が全て押さえられた

DEAR exp. for kaonic hydrogen atom G. Beer et al. , Phys. Rev. Lett. 94, 212302 (2005) Kaonic hydrogen atom, 1 sのレベルシフト @ DEAR Collaboration, DAΦNE, Frascati National Laboratories cf) KEK exp. M. Iwasaki et al. , Phys. Rev. Lett. 78, 3067 (1997) シフトの符号は同じだが、ＫＥＫの前回の実験（ＫｐＸ）と重ならない KEK exp. DEAR Coupled channel chiral dynamics (Chiral unitary model) で DEARの結果を合わすのには苦労する。 かろうじてギリギリ合わせられる程度。。。 B. Borasoy et al. , Phys. Rev. Lett. 94, 213401 (2005)

SHIDDARTA exp. for kaonic hydrogen atom M. Bazzi et al. , Phys. Lett. B 704, 113 (2011) Kaonic hydrogen atom, 1 sのレベルシフト @ SHIDDARTA Collaboration, DAΦNE, Frascati National Laboratories K-p散乱長が精密に決定 理論計算にとって重要な インプットに強い拘束条件 Kbar. N subthresholdでの 散乱振幅の振る舞い、 Λ(1405)のポールの位置、 が制限される。 KEK実験（ＫｐＸ）とコンシステントな結果 Y. Ikeda, T. Hyodo and W. Weise, Phys. Lett. B 706, 63 (2011)

Ｋ原子核に関係する実験 u Ｋ原子 (Kaonic atom) • Kaonic 4 He atom, 2 pレベルシフト (3 d→ 2 p X線測定) @ KEK (E 570) S. Okada et. al. , Phys. Lett. B 653, 387 (2007) • Kaonic 3 He atom, 2 pレベルシフト (3 d→ 2 p X線測定) @ J-PARC (E 17, DAY-1) • Kaonic hydrogen atom, 1 sレベルシフト @ DEAR group, DAΦNE, G. Beer et al. , Phys. Rev. Lett. 94, 212302 (2005) Frascati National Laboratories • Kaonic hydrogen, deuterium @ SIDDHARTA group M. Bazzi et al. , Phys. Lett. B 704, 113 (2011) u Λ(1405) πΣ invariant mass測定 γ + p → K+ + Λ(1405), Λ(1405) → π Σ • LEPS / SPring-8 J. K. Ahn, Nucl. Phys. A 835, 329 (2010) K. Moriya and R. Schumacher, Nucl. Phys. A 835, 325 (2010) • CLAS / JLab π-Σ+, π0Σ 0, π+Σ- が全て押さえられた

KEK E 570 for kaonic 4 He atom S. Okada et. al. , Phys. Lett. B 653, 387 (2007) Kaonic 4 He atom, 2 pのレベルシフト 3 d→ 2 p X線測定 @ KEK, E 570 “Kaonic helium puzzle” 理論の予言がほぼ 0 e. Vに対して、 過去の実験ではシフトは平均-43 e. V S. Hirenzaki et al. , Phys. Rev. C 61, 055205 (2000) シフトは 0 e. V とconsisitent パズルは解けた！

Ｋ原子核に関係する実験 u Ｋ原子 (Kaonic atom) • Kaonic 4 He atom, 2 pレベルシフト (3 d→ 2 p X線測定) @ KEK (E 570) S. Okada et. al. , Phys. Lett. B 653, 387 (2007) • Kaonic 3 He atom, 2 pレベルシフト (3 d→ 2 p X線測定) @ J-PARC (E 17, DAY-1) • Kaonic hydrogen atom, 1 sレベルシフト @ DEAR group, DAΦNE, G. Beer et al. , Phys. Rev. Lett. 94, 212302 (2005) Frascati National Laboratories • Kaonic hydrogen, deuterium @ SIDDHARTA group M. Bazzi et al. , Phys. Lett. B 704, 113 (2011) u Λ(1405) πΣ invariant mass測定 γ + p → K+ + Λ(1405), Λ(1405) → π Σ • LEPS / SPring-8 J. K. Ahn, Nucl. Phys. A 835, 329 (2010) K. Moriya and R. Schumacher, Nucl. Phys. A 835, 325 (2010) • CLAS / JLab π-Σ+, π0Σ 0, π+Σ- が全て押さえられた

Λ(1405) - πΣ invariant mass 測定 • LEPS / Spring-8 • CLAS / Jefferson Laboratory J. K. Ahn, Nucl. Phys. A 835, 329 (2010) K. Moriya and R. Schumacher, Nucl. Phys. A 835, 325 (2010) p (γ, K+ π) Σ at Eγ = 1. 5 -2. 4 Ge. V Charged πΣを測定 γ + p → K+ + Λ(1405), Λ(1405) → π Σ 三つの異なる電荷状態が抑えられた 理論 ピークの順番が理論 (chiral unitary)と違う？ Highest peak 実験：　Σ+ π理論：　Σ- π+

Experiments for K pp search

Ｋ原子核に関係する実験 u Ｋ原子核 (Kaonic nuclei) K-pp search • K- absorption on various targets / Invariant mass Λp @ FINUDA collaboration, DAΦNE, Frascati National Laboratories M. Angello et. al. , Phys. Rev. Lett. 94, 212303 (2005) • Heavy ion collision (? +? ) / Invariant mass Λp @ FOPI group, GSI N. Herrmann, Proc. of EXA’ 05, Austrian Academy of Sciences Press, (2005), p 73 • Anti-proton annihilation on 4 He / Invariant mass Λp @ OBELIX group, CERN G. Bendiscioli et. al. , Nucl. Phys. A 789, 222 (2007) • p+p -> K+ + Λ + p / Invariant mass Λp @ DISTO group, SATURNE, Saclay T. Yamazaki et. al. , Phys. Rev. Lett. 104, 132502 (2010) K-ppn search Search for heavier kaonic nuclei • 4 He (Stopped K-, n), 4 He (Stopped K-, p) / Mssing mass @ KEK-E 471, E 549 M. Sato et. al. , Phys. Lett. B 659, 107 (2008), H. Yim et. al. , Phys. Lett. B 688, 43 (2010) • 16 O (in-flight K-, n) 15 OK- / Missing mass @ AGS, BNL • 12 C (in-flight K -, T. Kishimoto et. al. , Nucl. Phys. A 754, 383 (2005) n or p) / Missing mass @ KEK-E 548 T. Kishimoto et. al. , Prog. Theor. Phys. Suppl. 168, 573 (2007)

Ｋ原子核に関係する実験 u Ｋ原子核 (Kaonic nuclei) K-pp search • K- absorption on various targets / Invariant mass Λp @ FINUDA collaboration, DAΦNE, Frascati National Laboratories M. Angello et. al. , Phys. Rev. Lett. 94, 212303 (2005) • Heavy ion collision (? +? ) / Invariant mass Λp @ FOPI group, GSI N. Herrmann, Proc. of EXA’ 05, Austrian Academy of Sciences Press, (2005), p 73 • Anti-proton annihilation on 4 He / Invariant mass Λp @ OBELIX group, CERN G. Bendiscioli et. al. , Nucl. Phys. A 789, 222 (2007) • p+p -> K+ + Λ + p / Invariant mass Λp @ DISTO group, SATURNE, Saclay T. Yamazaki et. al. , Phys. Rev. Lett. 104, 132502 (2010) K-ppn search Search for heavier kaonic nuclei • 4 He (Stopped K-, n), 4 He (Stopped K-, p) / Mssing mass @ KEK-E 471, E 549 M. Sato et. al. , Phys. Lett. B 659, 107 (2008), H. Yim et. al. , Phys. Lett. B 688, 43 (2010) • 16 O (in-flight K-, n) 15 OK- / Missing mass @ AGS, BNL • 12 C (in-flight K -, T. Kishimoto et. al. , Nucl. Phys. A 754, 383 (2005) n or p) / Missing mass @ KEK-E 548 T. Kishimoto et. al. , Prog. Theor. Phys. Suppl. 168, 573 (2007)

Experiments related to K-pp • FINUDA collaboration (DAΦNE, Frascatti) • K- absorption at rest on various nuclei (6 Li, 7 Li, 12 C, 27 Al, 51 V) • Invariant-mass method p K- p p If it is K-pp, … Total binding energy = 115 Λ Decay width = 67 Strong correlation between emitted p and Λ (back-to-back) Me. V Invariant mass of p and Λ PRL 94, 212303 (2005)

Experiments related to K-pp • Re-analysis of KEK-PS E 549 - K- stopped on 4 He target - Λp invariant mass Strong Λp back-to-back correlation is confirmed. Unknown strength is there in the same energy region as FINUDA. T. Suzuki et al (KEK-PS E 549 collaboration), ar. Xiv: 0711. 4943 v 1[nucl-ex] • DISTO collaboration - p + p -> K+ + Λ + p @ 2. 85 Ge. V - Λp invariant mass - Comparison with simulation data K- pp? ? ? B. E. = 103 ± 5 Me. V Γ = 118 ± 10 Me. V T. Yamazaki et al. (DISTIO collaboration), PRL 104, 132502 (2010)

What is the object observed experimentally? • DISTO collaboration A bound state of K-pp, or another object such as πΣN ? ? ? Only what we can say from only this spectrum is that “There is some object with B=2, S=-1, charge=+1”…

J-PARC will give us lots of interesting data! E 15: A search for deeply bound kaonic nuclear states by 3 He(inflight K-, n) reaction --- Spokespersons: M. Iwasaki (RIKEN), T. Nagae (Kyoto) E 17: Precision spectroscopy of kaonic 3 He atom 3 d→ 2 p X-rays --- Spokespersons: R. Hayano (Tokyo), H. Outa (Riken)

J-PARC will give us lots at K 1. 8 BR beamof line interesting data! 1. 8 Ge. V/c E 15: A search for deeply bound kaonic nuclear states by 3 He(inflight K-, n) reaction --- Spokespersons: M. Iwasaki (RIKEN), T. Nagae (Kyoto) E 17: Precision spectroscopy of kaonic 3 He atom 3 d→ 2 p X-rays Dr. Fujioka’s talk --- Spokespersons: R. Hayano (Tokyo), H. Outa (KEK(Riken) workshop, 7 -9. Aug. 08)

Invariant mass J-PARC will give us lots at K 1. 8 BR beamof spectroscopyline interesting data! 1. 8 Ge. V/c Missing E 15: A search for deeply bound kaonic nuclear states by 3 He(inflight K-, n) reaction mass spectroscopy --- Spokespersons: M. Iwasaki (RIKEN), T. Nagae (Kyoto) E 17: Precision spectroscopy of kaonic 3 He atom All emitted 3 d→ 2 pparticles X-rays will be measured. Dr. Fujioka’s talk --- Spokespersons: R. Hayano (Tokyo), H. Outa (KEK(Riken) workshop, 7 -9. Aug. 08) 　　「完全実験」

Preceding E 15, E 27 experiment will be performed in June. E 27: d (π+, K+) K-pp at K 1. 8 beam line Missing mass measured. K+ π+ d n p Λ(1405) Kp p

5. Summary and Future plan

5. Summary Kaonic nuclei are exotic system !? • Kaonic nuclei are another form of nuclear system involving strangeness. They might be exotic system because of the strong attraction of I=0 Kbar. N potential. • AMD calculation with G-matrix method using a phenomenological Kbar. N potential (AY potential) shows that kaonic nuclei may have lots of interesting properties: Deeply bound and narrow width dense system with interesting structure… • However, these properties have not been established and there are some questions. Variational calc. of K-pp with a chiral SU(3)-based Kbar. N pot. • B. E. =20± 3 Me. V, Γ(Kbar. NN → πYN) = 40 – 70 Me. V • With p-wave Kbar. N pot. , dispersion correction, and two-nucleon absorption, B. E. =20 – 40 Me. V, Γ = 55 – 120 Me. V • Two protons distance = 2. 0 fm ≒NN mean distance of normal nucleus • Λ(1405) structure (correlation) remains in K-pp is a shallowly bound and not so dense system.

5. Summary Current status of studies of K-pp The most essential Kbar nuclei “K-pp” (Kbar. NN, Jp=1/2 -, T=0) has been investigated in various ways. But the situation is still controversial… Theory Variational Faddeev + + Phenom. Kbar. N Chiral-based Kbar. N B. E. = 47 Me. V, B. E. = 20± 3 Me. V, B. E. = 50～ 70 Me. V, B. E. = 60～ 95 Me. V, Γ= 61 Me. V Γ= 40～ 70 Me. V Γ=～ 100 Me. V Γ= 45～ 80 Me. V PRC 76, 045201(2007) PRC 79, 014003(2009) PRC 76, 044004(2007) PRC 76, 035203(2007) Experiment (Unknown object which seems related to K-pp) FINUDA DISTO B. E. = 115 Me. V, B. E. = 103 Me. V, Γ= 67 Me. V Γ= 118 Me. V PRL 94, 212303(2005) PRL 104, 132502 (2010) Discrepancy between theoretical studies of K-pp • DHW (Variational with Chiral-based) vs AY (Variational with phenomenological) … Difference of Kbar. N attraction Λ(1420) scheme and Λ(1405) scheme • DHW (Variational with Chiral-based) vs IS (Faddeev with Chiral-based) … πΣN three-body dynamics (might be also different energy dependence of interaction kernel? )

5. Future plan Studied with coupled-channel Complex Scaling Method Direct treatment of πΣN degree in K-pp. Deal with a resonant state, based on variational scheme. • πΣN dynamics as pointed out by Dr. Ikeda and Prof. Sato. • The signal position of DISTO experiment … very close to π+Σ+N threshold Go to charm sector! K- (subar) D 0 (cubar) 494 Me. V 1870 Me. V Do D-mesic nuclei exist such as DNN analog to Kbar. NN? ? ? M. Bayar, C. W. Xiao, T. Hyodo, A. Dote, M. Oka, E. Oset, ar. Xiv: 1205. 2275 [hep-ph]

Thank you for your attention!

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